Fuzzy Quantifiers - Glöckner, Ingo

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Résumé :
From a linguistic perspective, it is quanti?cation which makes all the di?- ence between ?having no dollars? and ?having a lot of dollars?. And it is the meaning of the quanti?er ?most? which eventually decides if ?Most Ame- cans voted Kerry? or ?Most Americans voted Bush? (as it stands). Natural language(NL)quanti?erslike?all?,?almostall?,?many?etc. serveanimp- tant purpose because they permit us to speak about properties of collections, as opposed to describing speci?c individuals only; in technical terms, qu- ti?ers are a ?second-order? construct. Thus the quantifying statement ?Most Americans voted Bush? asserts that the set of voters of George W. Bush c- prisesthemajorityofAmericans,while?Bushsneezes?onlytellsussomething about a speci?c individual. By describing collections rather than individuals, quanti?ers extend the expressive power of natural languages far beyond that of propositional logic and make them a universal communication medium. Hence language heavily depends on quantifying constructions. These often involve fuzzy concepts like ?tall?, and they frequently refer to fuzzy quantities in agreement like ?about ten?, ?almost all?, ?many? etc. In order to exploit this expressive power and make fuzzy quanti?cation available to technical applications, a number of proposals have been made how to model fuzzy quanti?ers in the framework of fuzzy set theory. These approaches usually reduce fuzzy quanti?cation to a comparison of scalar or fuzzy cardinalities [197, 132].

Biographie:
Ingo Gl?ckner received his M.A. in Computational Linguistics and Artificial Intelligence from University of Osnabr?ck in 1996. He then became a research assistant at the University of Bielefeld, where he pursued research on fuzzy set theory and its application to information retrieval. In 2003, I. Gl?ckner received his PhD for his thesis on the semantical interpretation and implementation of fuzzy quantifiers. He then joined the Intelligent Information and Communication Systems Group (Prakt. Informatik VII) of Prof. H. Helbig at the FernUniversit?t in Hagen. His current research activities are centered on the representation and processing of knowledge expressed in natural language....

Sommaire:
An Introduction to Fuzzy Quantification: Origins and Basic Concepts.- A Framework for Fuzzy Quantification.- The Axiomatic Class of Plausible Models.- Semantic Properties of the Models.- Special Subclasses of Models.- Special Semantical Properties and Theoretical Limits.- Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation.- Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts.- The Full Class of Models Defined in Terms of Three-Valued Cuts.- The Class of Models Based on the Extension Principle.- Implementation of Quantifiers in the Models.- Multiple Variable Binding and Branching Quantification.- Discussion.